Essentially the best way to think of "Objects" is by comparing it to the Outliner window in Maya. Say you want to create a Sphere... you would create a geometry operator in objects, and then jump inside it and create your sphere... Kind of similar to if you were to create a Null in Maya, and then parent a sphere to it. You typically want to do a lot of your animation at the object level... do your global animation there.
It can seem tricky, because there are different types of networks (Geometry, Dynamics, Particles, Compositing, Rendering... etc) which you can access from any point... by placing networks within networks though things can actually get very neat and organized.
Objects are a type of operator. All operators have their own functionability. The difference between Houdini and Maya etc. is that Houdini lets you have access to the operators, so you can build your own tools, where as the other programs give you the tools and pretend that what you want can't be done another way. Being able to disassemble and rearrange operators any way you want essentially makes it so that you rarely back yourself into a corner, and can always experiment yet still retain your old results.